Part II. Molecular Dynamics Calculations

Potassium Ions

Ions in electrolyte solutions are not free but hydrated with the first
shell relatively firmly bound, followed by a more loosely bound second
shell.

For potassium ions, there are on average about 7 water molecules in
the first hydration shell, lying at around 2.8 angstrom from the ion
centre. Each of these waters stabilizes the ion by approximately 24
kT.

Thus, the apparent radius of a potassium ion is far too large
to pass across the selectivity filter unless the water-ion geometry is
re-arranged.

As the ion enters the selectivity filter, some of the tightly bound
water molecules are stripped off. To prevent the insurmountable
energy cost involved with this loss, the carbonyl oxygen atoms play
the role of the water molecules by forming temporary bonds with the
potassium ion.

The ion-water geometry can be deduced more rigorously by examining
what is commonly known as the radial distribution function. Here, the
probability of finding oxygen atoms is plotted against the distance
from the centre of the potassium ion.

The peak in the radial distribution function due to water
contributions, shown here in pink, is becoming smaller as water
molecules become less accessible, while the peak corresponding to
carbonyl oxygens, shown here in orange, is approaching and becoming
larger as the ion enters the selectivity filter.

Through most of the selectivity filter, the potassium ion in
surrounded by carbonyl oxygen atoms and water molecules such that the
two peaks in the radial distribution function are roughly
superimposed. This demonstrates how well the carbonyl groups are able
to emulate water molecules.

The perfectly overlapping electron clouds of the potassium ion and
carbonyl oxygens explains how this ion is able to traverse the narrow
segment of the potassium channel.

Sodium Ions

Consider now a sodium ion attempting to traverse the selectivity
filter. As it enters, waters are stripped away, as they are for
potassium.

However, due to the smaller ion size, the carbonyl oxygen atoms are
unable to replace water molecules as effectively. As a result the
sodium ion is ejected from the filter. Observe the two peaks in the
radial distribution function as we push a sodium ion through.

Carbonyl oxygens are unable to come close enough to the sodium ion to
behave as water molecules. The oxygens are held away from the ion by
the molecular springs created by interactions with external protein
sidechains. Observe the poor fit of oxygen atoms around the ion.

When we compare to the potassium ion we can understand how this
channel discriminates between these two ions. Clearly the protein
cannot admit the passage of a sodium ion due to the energy barrier
faced as a result of solvation losses.

The channel therefore relies on the differing sizes of the potassium
and sodium ions to obtain selectivity. The dimensions of the
selectivity filter have been perfectly optimised by nature to achieve
this outcome.